TABLE OF CONTENTS In this chapter we summarize the three-dimensional equations of the nonlinear theory of electroelasticty for large deformations and strong fields [1, 2], the linear theory of piezoelectricity for infinitesimal deformation and fields [3, 4], the linear theory for small fields superposed on finite biasing or initial fields [5, 6, 7], and the theory for weak, cubic nonlinearity [8, 9]. A systematic presentation of these theories can also be found in [10]. This chapter uses the two-point Cartesian tensor notation, the summation convention for repeated tensor indices, and the convention that a comma followed by an index denotes partial differentiation with respect to the coordinate associated with the index.
Consider a deformable continuum which, in the reference configuration at time t 0, occupies a region V with a boundary surface S (see Fig. 1.1.1). N is the unit exterior normal of S. In this state the body is free from deformation and fields. The position of a material point in this state is denoted by a vector X= X K I K in a rectangular coordinate system X K where X K denotes the reference or material coordinates of the material point. They form a continuous labeling of material particles so that they are identifiable. At time t, the body occupies a region v with a boundary surface s and an exterior normal n. The current position of the material point associated...
